Question

2. 2x (y + 1) dx - y dy=0.​

Answer 1

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Class 12

>>Maths

>>Differential Equations

>>Solving Linear Differential Equation

>>y^2 + ( x - 1/y )dy/dx = 0. | Maths Que

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y

2

+(x−

y

1

)

dx

dy

=0.

Easy

Solution

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Correct option is B)

y

2

+(x−

y

1

)

dx

dy

=0

⇒

dy

dx

+

y

2

1

x=

y

3

1

. ...(1)

Let P=

y

2

1

⇒∫PdP=∫

y

2

1

dy=−

y

1

∴ I.F. μ=e

∫PdP

=e

−

y

1

Multiplying (1) by I.F. we get

e

−

y

1

dy

dx

+e

−

y

1

y

2

1

x=e

−

y

1

y

3

1

Integrating both sides, we get

x.e

−1/y

=∫

y

1

.

y

2

1

e

−1/y

.dy+c

⇒xe

t

=−∫te

t

dt+c=−(t−1)e

t

+c.

∴x=−(t−1)+ce

−t

where t=1/y